Question: The lifespans of snakes in a particular zoo are normally distributed. The average snake lives $21.8$ years; the standard deviation is $3.8$ years. Use the empirical rule (68-95-99.7%) to estimate the probability of a snake living between $10.4$ and $25.6$ years.
Explanation: $21.8$ $18$ $25.6$ $14.2$ $29.4$ $10.4$ $33.2$ $99.7\%$ $68\%$ $15.85\%$ $15.85\%$ We know the lifespans are normally distributed with an average lifespan of $21.8$ years. We know the standard deviation is $3.8$ years, so one standard deviation below the mean is $18$ years and one standard deviation above the mean is $25.6$ years. Two standard deviations below the mean is $14.2$ years and two standard deviations above the mean is $29.4$ years. Three standard deviations below the mean is $10.4$ years and three standard deviations above the mean is $33.2$ years. We are interested in the probability of a snake living between $10.4$ and $25.6$ years. The empirical rule (or the 68-95-99.7 rule) tells us that $99.7\%$ of the snakes will have lifespans within 3 standard deviations of the average lifespan. It also tells us that $68\%$ of the snakes will have lifespans within 1 standard deviation of the mean. The probability of a particular snake living between $10.4$ and $25.6$ years is $\color{orange}{15.85\%} + {68\%}$, or $83.85\%$.